Experimental Study on Vortex-Induced Vibration of Rough Risers Coupling with Interference Effect in Tandem Arrangement

In order to study the response law of vortex-induced vibration(VIV)of marine risers under the combined action of roughness and interference effects,and to reveal the coupling mechanism of roughness and interference effects on the riser,a VIV experiment of rough risers in tandem arrangement was conducted in a wave−current combined flume.The experiment characterized the risers’roughness by arranging different specifications of attachments on the surface of the risers.Three rough risers with different roughness and smooth risers were arranged in tandem arrangement,with the rough risers arranged downstream.The experimental results indicate that the suppression of the attachments on the downstream risers’vibration are more significant both in the CF and IL directions as the reduced velocity increases.For the downstream riser,the amplitude response of rough riser is more significantly weakened compared with the smooth one at high reduced velocity.For the upstream risers,changes in the roughness and spacing ratio have an impact on their‘lock-in’region.When the roughness of downstream risers is relatively large(0.1300)and the spacing between risers is small(S/D=4.0),the reduced velocity range of‘lock-in’region in the CF direction of upstream risers is obviously expanded,and the displacement in the‘lock-in’region is severer.

Shear behavior and off-fault damage of saw-cut smooth and tension-induced rough joints in granite

The damage of rock joints or fractures upon shear includes the surface damage occurring at the contact asperities and the damage beneath the shear surface within the host rock.The latter is commonly known as off-fault damage and has been much less investigated than the surface damage.The main contribution of this study is to compare the results of direct shear tests conducted on saw-cut planar joints and tension-induced rough granite joints under normal stresses ranging from 1 MPa to 50 MPa.The shear-induced off-fault damages are quantified and compared with the optical microscope observation.Our results clearly show that the planar joints slip stably under all the normal stresses except under 50 MPa,where some local fractures and regular stick-slip occur towards the end of the test.Both post-peak stress drop and stick-slip occur for all the rough joints.The residual shear strength envelopes for the rough joints and the peak shear strength envelope for the planar joints almost overlap.The root mean square(RMS)of asperity height for the rough joints decreases while it increases for the planar joint after shear,and a larger normal stress usually leads to a more significant decrease or increase in RMS.Besides,the extent of off-fault damage(or damage zone)increases with normal stress for both planar and rough joints,and it is restricted to a very thin layer with limited micro-cracks beneath the planar joint surface.In comparison,the thickness of the damage zone for the rough joints is about an order of magnitude larger than that of the planar joints,and the coalesced micro-cracks are generally inclined to the shear direction with acute angles.The findings obtained in this study contribute to a better understanding on the frictional behavior and damage characteristics of rock joints or fractures with different roughness.

Experimental Study on Vortex-Induced Vibration of Rough Risers with Coupling Interference Effect Under Side-by-Side Arrangement

A vortex-induced vibration(VIV)experiment of rough risers with coupling interference effect under a side-by-side arrangement was carried out in a wave-current combined flume.The roughness of the riser was characterized by arranging different specifications of surface attachments on the surface of the riser.Rough risers with three different roughnesses were arranged side by side with smooth risers to explore the VIV response of the riser under the combined action of roughness and interference effect,and to reveal the coupling mechanism between roughness and interference effect.The experimental results show that,compared with that of a smooth riser,the VIV of a rough riser under the coupling interference effect has a wider"lock-in"region,and the displacement decreases more significantly at a high reduced velocity,which is more likely to excite higher-order modes and frequency responses.In addition,the displacement response and frequency response of the smooth riser are not significantly affected by wake interference from the rough riser,which is caused by the decrease of the wake region due to the delay of the boundary layer separation point of the rough riser.

Enhancing the anti-corrosion performance and biocompatibility of AZ91D Mg alloy by applying roughness pretreatment and coating with in-situ Mg(OH)_(2)/Mg-Al LDH

Corrosion-resistant and biocompatible films were fabricated on AZ91D Mg alloy substrates by varying their roughness levels using met-allographic preparation and subsequent hydrothermal procedures.The coated films comprised a mixed structure of Mg(OH)_(2)and Mg-Al layered double hydroxides(LDH)and exhibited excellent compactness.Coating film thickness increased with decreasing surface roughness.Corrosion resistance was evaluated using potentiodynamic polarization and electrochemical impedance spectroscopy.Metallographic pretreat-ment influenced the chemical activity of the Mg alloy surface and helped modulate the dissolution rate of the Mg_(17)Al_(12)phase during the hydrothermal procedure.With decreasing roughness of the Mg substrate,the Al^(3+)concentration gradually increased,accelerating the in-situ formation of the Mg(OH)_(2)/LDH composite coating and improving its crystallinity.A thick and dense Mg(OH)_(2)/LDH coating was synthesized on the Mg substrate with the least roughness,substantially improving the corrosion resistance of the AZ91D alloy.The lowest corrosion current density((5.73±2.75)×10^(−8)A·cm^(−2))was achieved,which was approximately three orders of magnitude less than that of bare AZ91D.Moreover,the coating demonstrated biocompatibility with no evident cytotoxicity,cellular damage,and hemolytic phenomena.This study provides an effective method for preparing coatings on Mg alloy surfaces with excellent corrosion resistance and biocompatibility.

Complex Decision Modeling Framework with Fairly Operators and Quaternion Numbers under Intuitionistic Fuzzy Rough Context

The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.

Roughness characterization and shearing dislocation failure for rock-backfill interface

Shearing dislocation is a common failure type for rock–backfill interfaces because of backfill sedimentation and rock strata movement in backfill mining goaf.This paper designed a test method for rock–backfill shearing dislocation.Using digital image techno-logy and three-dimensional(3D)laser morphology scanning techniques,a set of 3D models with rough joint surfaces was established.Further,the mechanical behavior of rock–backfill shearing dislocation was investigated using a direct shear test.The effects of interface roughness on the shear–displacement curve and failure characteristics of rock–backfill specimens were considered.The 3D fractal dimen-sion,profile line joint roughness coefficient(JRC),profile line two-dimensional fractal dimension,and the surface curvature of the frac-tures were obtained.The correlation characterization of surface roughness was then analyzed,and the shear strength could be measured and calculated using JRC.The results showed the following:there were three failure threshold value points in rock–backfill shearing dis-location:30%–50%displacement before the peak,70%–90%displacement before the peak,and 100%displacement before the peak to post-peak,which could be a sign for rock–backfill shearing dislocation failure.The surface JRC could be used to judge the rock–backfill shearing dislocation failure,including post-peak sliding,uniform variations,and gradient change,corresponding to rock–backfill disloca-tion failure on the field site.The research reveals the damage mechanism for rock–backfill complexes based on the free joint surface,fills the gap of existing shearing theoretical systems for isomerism complexes,and provides a theoretical basis for the prevention and control of possible disasters in backfill mining.

Maximal operators of pseudo-differential operators with rough symbols

Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.

Influence of Surface Ice Roughness on the Aerodynamic Performance of Wind Turbines

The focus of this research was on the equivalent particle roughness height correction required to account for the presence of ice when determining the performances of wind turbines.In particular,two icing processes(frost ice and clear ice)were examined by combining the FENSAP-ICE and FLUENT analysis tools.The ice type on the blade surfaces was predicted by using a multi-time step method.Accordingly,the influence of variations in icing shape and ice surface roughness on the aerodynamic performance of blades during frost ice formation or clear ice formation was investigated.The results indicate that differences in blade surface roughness and heat flux lead to disparities in both ice formation rate and shape between frost ice and clear ice.Clear ice has a greater impact on aerodynamics compared to frost ice,while frost ice is significantly influenced by the roughness of its icy surface.

Proppant transport in rough fracture networks using supercritical CO_(2)

Proppant transport within fractures is one of the most critical tasks in oil,gas and geothermal reservoir stimulation,as it largely determines the ultimate performance of the operating well.Proppant transport in rough fracture networks is still a relatively new area of research and the associated transport mechanisms are still unclear.In this study,representative parameters of rough fracture surfaces formed by supercritical CO_(2) fracturing were used to generate a rough fracture network model based on a spectral synthesis method.Computational fluid dynamics(CFD)coupled with the discrete element method(DEM)was used to study proppant transport in this rough fracture network.To reveal the turning transport mechanism of proppants into branching fractures at the intersections of rough fracture networks,a comparison was made with the behavior within smooth fracture networks,and the effect of key pumping parameters on the proppant placement in a secondary fracture was analyzed.The results show that the transport behavior of proppant in rough fracture networks is very different from that of the one in the smooth fracture networks.The turning transport mechanisms of proppant into secondary fractures in rough fracture networks are gravity-driven sliding,high velocity fluid suspension,and fracture structure induction.Under the same injection conditions,supercritical CO_(2)with high flow Reynolds number still has a weaker ability to transport proppant into secondary fractures than water.Thickening of the supercritical CO_(2)needs to be increased beyond a certain value to have a significant effect on proppant carrying,and under the temperature and pressure conditions of this paper,it needs to be increased more than 20 times(about 0.94 m Pa s).Increasing the injection velocity and decreasing the proppant concentration facilitates the entry of proppant into the branching fractures,which in turn results in a larger stimulated reservoir volume.The results help to understand the proppant transport and placement process in rough fracture networks formed by reservoir stimulation,and provide a theoretical reference for the optimization of proppant pumping parameters in hydraulic fracturing.

Theoretical Modeling and Surface Roughness Prediction of Microtextured Surfaces in Ultrasonic Vibration-Assisted Milling

Textured surfaces with certain micro/nano structures have been proven to possess some advanced functions,such as reducing friction,improving wear and increasing wettability.Accurate prediction of micro/nano surface textures is of great significance for the design,fabrication and application of functional textured surfaces.In this paper,based on the kinematic analysis of cutter teeth,the discretization of ultrasonic machining process,transformation method of coordinate systems and the cubic spline data interpolation,an integrated theoretical model was established to characterize the distribution and geometric features of micro textures on the surfaces machined by different types of ultrasonic vibration-assisted milling(UVAM).Based on the theoretical model,the effect of key process parameters(vibration directions,vibration dimensions,cutting parameters and vibration parameters)on tool trajectories and microtextured surface morphology in UVAM is investigated.Besides,the effect of phase difference on the elliptical shape in 2D/3D ultrasonic elliptical vibration-assisted milling(UEVAM)was analyzed.Compared to conventional numerical models,the method of the cubic spline data interpolation is applied to the simulation of microtextured surface morphology in UVAM,which is more suitable for characterizing the morphological features of microtextured surfaces than traditional methods due to the presence of numerous micro textures.The prediction of surface roughness indicates that the magnitude of ultrasonic amplitude in z-direction should be strictly limited in 1D rotary UVAM,2D and 3D UEVAM due to the unfavorable effect of axial ultrasonic vibration on the surface quality.This study can provide theoretical guidance for the design and fabrication of microtextured surfaces in UVAM.

RB-DEM Modeling and Simulation of Non-Persisting Rough Open Joints Based on the IFS-Enhanced Method

When the geological environment of rock masses is disturbed,numerous non-persisting open joints can appear within it.It is crucial to investigate the effect of open joints on the mechanical properties of rock mass.However,it has been challenging to generate realistic open joints in traditional experimental tests and numerical simulations.This paper presents a novel solution to solve the problem.By utilizing the stochastic distribution of joints and an enhanced-fractal interpolation system(IFS)method,rough curves with any orientation can be generated.The Douglas-Peucker algorithm is then applied to simplify these curves by removing unnecessary points while preserving their fundamental shape.Subsequently,open joints are created by connecting points that move to both sides of rough curves based on the aperture distribution.Mesh modeling is performed to construct the final mesh model.Finally,the RB-DEM method is applied to transform the mesh model into a discrete element model containing geometric information about these open joints.Furthermore,this study explores the impacts of rough open joint orientation,aperture,and number on rock fracture mechanics.This method provides a realistic and effective approach for modeling and simulating these non-persisting open joints.

High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.

On Multi-Granulation Rough Sets with Its Applications

Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.

Characteristics of proppant transport and placement within rough hydraulic fractures

A three-dimensional reconstruction of rough fracture surfaces of hydraulically fractured rock outcrops is carried out by casting process,a large-scale experimental setup for visualizing rough fractures is built to perform proppant transport experiments.The typical characteristics of proppant transport and placement in rough fractures and its intrinsic mechanisms are investigated,and the influences of fracture inclination,fracture width and fracturing fluid viscosity on proppant transport and placement in rough fractures are analyzed.The results show that the rough fractures cause variations in the shape of the flow channel and the fluid flow pattern,resulting in the bridging buildup during proppant transport to form unfilled zone,the emergence of multiple complex flow patterns such as channeling,reverse flow and bypassing of sand-carrying fluid,and the influence on the stability of the sand dune.The proppant has a higher placement rate in inclined rough fractures,with a maximum increase of 22.16 percentage points in the experiments compared to vertical fractures,but exhibits poor stability of the sand dune.Reduced fracture width aggravates the bridging of proppant and induces higher pumping pressure.Increasing the viscosity of the fracturing fluid can weaken the proppant bridging phenomenon caused by the rough fractures.

Mechanical properties and fracture surface roughness of thermally damaged granite under dynamic splitting

In order to understand the mechanical properties and the fracture surface roughness characteristics of thermally damaged granite under dynamic splitting,dynamic Brazilian splitting tests were conducted on granite samples after thermal treatment at 25,200,400,and 600℃.Results show that the dynamic peak splitting strength of thermally damaged granite samples increases with increasing strain rate,showing obvious strain‐rate sensitivity.With increasing temperature,thermally induced cracks in granite transform from intergranular cracks to intragranular cracks,and to a transgranular crack network.Thermally induced damages reduce the dynamic peak splitting strength and the maximum absorbed energy while increasing the peak radial strain.The fracture mode of the thermally damaged granite under dynamic loads is mode Ⅱ splitting failure.By using the axial roughness index Z2 a,the distribution ranges of the wedge‐shaped failure zones and the tensile failure zones in the fracture surfaces under dynamic Brazilian splitting can be effectively identified.The radial roughness index Z_(2)^(r)is sensitive to the strain rate and temperature.It shows a linear correlation with the peak splitting strength and the maximum absorbed energy and a linear negative correlation with the peak radial strain.Z_(2)^(r)can be used to quantitatively estimate the dynamic parameters based on the models proposed.

Shear mechanical properties and fracturing responses of layered rough jointed rock-like materials

This study aims to investigate mechanical properties and failure mechanisms of layered rock with rough joint surfaces under direct shear loading.Cubic layered samples with dimensions of 100 mm×100 mm×100 mm were casted using rock-like materials,with anisotropic angle(α)and joint roughness coefficient(JRC)ranging from 15°to 75°and 2-20,respectively.The direct shear tests were conducted under the application of initial normal stress(σ_(n))ranging from 1-4 MPa.The test results indicate significant differences in mechanical properties,acoustic emission(AE)responses,maximum principal strain fields,and ultimate failure modes of layered samples under different test conditions.The peak stress increases with the increasingαand achieves a maximum value atα=60°or 75°.Asσ_(n)increases,the peak stress shows an increasing trend,with correlation coefficients R²ranging from 0.918 to 0.995 for the linear least squares fitting.As JRC increases from 2-4 to 18-20,the cohesion increases by 86.32%whenα=15°,while the cohesion decreases by 27.93%whenα=75°.The differences in roughness characteristics of shear failure surface induced byαresult in anisotropic post-peak AE responses,which is characterized by active AE signals whenαis small and quiet AE signals for a largeα.For a given JRC=6-8 andσ_(n)=1 MPa,asαincreases,the accumulative AE counts increase by 224.31%(αincreased from 15°to 60°),and then decrease by 14.68%(αincreased from 60°to 75°).The shear failure surface is formed along the weak interlayer whenα=15°and penetrates the layered matrix whenα=60°.Whenα=15°,asσ_(n)increases,the adjacent weak interlayer induces a change in the direction of tensile cracks propagation,resulting in a stepped pattern of cracks distribution.The increase in JRC intensifies roughness characteristics of shear failure surface for a smallα,however,it is not pronounced for a largeα.The findings will contribute to a better understanding of the mechanical responses and failure mechanisms of the layered rocks subjected to shear loads.

Boulder-induced form roughness and skin shear stresses in a gravel-bed stream

Boulder spacing in mountain rivers and near-wake flow zones within the boulder array is very useful for fish habitat and growth of aquatic organisms.The present study aims to investigate how the boulder array and spacing influence the near-bed flow structures in a gravel-bed stream.Boulders are staggered over a gravel-bed stream with three different inter-boulder spacing namely(a)large(b)medium and(c)small spacing.An acoustic Doppler velocimeter was used for flow measurements in a rectangular channel and the results were compared with those acquired from numerical simulation.The time-averaged velocity profiles at the near-wake flow zones of boulders experience maximum flow retardation which is an outcome of the boulder-induced form roughness.The ratio of velocity differences associated to form and skin roughness and its positive magnitude reveals the dominance of form roughness closest to the boulders.Form roughness computed is 1.75 to 2 times higher than the skin roughness at the near-wake flow region.In particular,the collective immobile boulders placed at different inter-boulder spacings developed high and low bed shear stresses closest to the boulders.The low bed shear stresses characterised by a secondary peak developed at the trough location of the boulders is attributed to the skin shear stress.Further,the spatial averaging of time-averaged flow quantities gives additional impetus to present an improved illustration of fluid shear stresses.The formation of form-induced shear stress is estimated to be 17%to 23%of doubleaveraged Reynolds shear stress and partially compensates for the damping of time-averaged Reynolds shear stress in the interfacial sub-layer.The quadrant analysis of spatial velocity fluctuations depicts that the form-induced shear stresses are dominant in the interfacial sub-layer and have no significance above the gravel-bed surface.

Multi-Granularity Neighborhood Fuzzy Rough Set Model on Two Universes

The two universes multi-granularity fuzzy rough set model is an effective tool for handling uncertainty problems between two domains with the help of binary fuzzy relations. This article applies the idea of neighborhood rough sets to two universes multi-granularity fuzzy rough sets, and discusses the two-universes multi-granularity neighborhood fuzzy rough set model. Firstly, the upper and lower approximation operators are defined in the two universes multi-granularity neighborhood fuzzy rough set model. Secondly, the properties of the upper and lower approximation operators are discussed. Finally, the properties of the two universes multi-granularity neighborhood fuzzy rough set model are verified through case studies.

An ensemble learning method to retrieve sea ice roughness from Sentinel-1 SAR images

Sea ice surface roughness(SIR)affects the energy transfer between the atmosphere and the ocean,and it is also an important indicator for sea ice characteristics.To obtain a small-scale SIR with high spatial resolution,a novel method is proposed to retrieve SIR from Sentinel-1 synthetic aperture radar(SAR)images,utilizing an ensemble learning method.Firstly,the two-dimensional continuous wavelet transform is applied to obtain the spatial information of sea ice,including the scale and direction of ice patterns.Secondly,a model is developed using the Adaboost Regression model to establish a relationship among SIR,radar backscatter and the spatial information of sea ice.The proposed method is validated by using the SIR retrieved from SAR images and comparing it to the measurements obtained by the Airborne Topographic Mapper(ATM)in the summer Beaufort Sea.The determination of coefficient,mean absolute error,root-mean-square error and mean absolute percentage error of the testing data are 0.91,1.71 cm,2.82 cm,and 36.37%,respectively,which are reasonable.Moreover,K-fold cross-validation and learning curves are analyzed,which also demonstrate the method’s applicability in retrieving SIR from SAR images.

Pseudo-Semi-Overlap Functions-Based Fuzzy Rough Sets Applied to Image Edge Extraction

As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and further extended for applications in image edge extraction. Firstly, a new clustering function, the pseudo-semi-overlap function, is introduced by eliminating the symmetry and right continuity present in the overlap function. The relaxed nature of this function enhances its applicability in image edge extraction. Secondly, the definitions of (I, PSO)-fuzzy rough sets are provided, using (I, PSO)-fuzzy rough sets, a pair of new fuzzy mathematical morphological operators (IPSOFMM operators) is proposed. Finally, by combining the fuzzy C-means algorithm and IPSOFMM operators, a novel image edge extraction algorithm (FCM-IPSO algorithm) is proposed and implemented. Compared to existing algorithms, the FCM-IPSO algorithm exhibits more image edges and a 73.81% decrease in the noise introduction rate. The outstanding performance of (I, PSO)-fuzzy rough sets in image edge extraction demonstrates their practical application value.